Interaction of multiple parallel cracks in a pre-stressed orthotropic elastic plane

Pre-stressed structures have been widely applied in aerospace, deep mining, and civil engineering fields. This paper presents a theoretical analysis of the interaction of multiple parallel cracks in a pre-stressed orthotropic elastic material. The pseudo-traction method and complex potential method are applied to solve an associated mixed boundary-value problem. First, we derive two kinds of fundamental solutions for a pair of normal and tangential concentrated forces acting at any point on an isolated crack. Then, with these solutions, a system of Fredholm integral equations are derived by superposition. The interaction of multiple parallel cracks in a prestressed orthotropic elastic plane is analyzed. Numerical results show that the pre-stress has little influence on the stress intensity factors when two cracks are collinear or two cracks are far away from each other (D-h > 2a or D-v > 5a). For closer two parallel cracks, K-I decreases with increasing pre-stress sigma(0) under normal loading and K-II increases with increasing pre-stress sigma(0) under shear loading.